"cricket" sound after turning off shower

I've got a faucet (Delta I think) on my tub, one of those big plastic ball kinds that has the two washers-and-springs behind the ball (lift up to turn water on, turn left or right to adjust temperature). That part works fine, no leaks after moving the ball all the way down.

Below that is a rod that is the shower diverter. The shower head is a one of those basic shower massage head with a rubber hose.

So...I've noticed sometimes after I shower, it'll be quiet, but then a few minutes or later: for a few hours or a day I'll get a "cricket" off-and-on sound that maybe sounds like it's coming out of the plumbing in that bathroom by the tub. The faucet/spigot itself doesn't appear to leak at all once I put the ball all the way down.

Is this little off-and-on "cricket" noise a pressure thing after I shut if off? If I play with the diverter a little--moving the knob in and out--will it relieve pressure? The house is up for sale, so I'd rather not spend any money to fix it. Unless this like, totally, a huge deal. It doesn't do it all the tme, just sometimes.

Unless the diverter rod pops out as soon as you turn off the water, the cricket sound could be it popping out later. If so, it is sticking and should be replaced. Otherwise it could break, and when that happens the rod is ejected from the faucet and often hits you in a very sensitive part of your body.